A quick search took me to a study on red deer in Europe (Moyes et al., 2011, Global Change Biology). Among other things, they found that larger bulls did shed earlier, that bulls that shed earlier grew larger antlers in the following growing season, and that warm temperatures during the previous summer and the current winter moved the dates forward. So, have a warmer winter (like the one we're having now), and deer might shed a bit earlier. I'll have to poke around- it's an interesting question.